20 years ago I went on a ridealong with a bunch of men who were changing the times on the clocks installed in a bunch of church towers.

It was fascinating to get to watch the process. I'd always taken it for granted the big hotels, railway stations, and churches would often have big clocks you could see from a distance and that they'd be self-correcting. But of course a lot of old clocks are purely mechanical so when the time changed an hour forwards/backwards somebody would need to physically change them.

Even the clock in my car (2016) doesn't self correct. It goes ahead of about 1 minute every month.

How so? Clearly these guys have heard of NTP. They are talking about ns precision systems, not ms.